Question

# State whether the following statement is correct or incorrect. Write the correct form if the incorrect statement: $\phi \in \{ a,b\}$

Hint: You need to know what the symbol $\phi$ denotes. Then you need to analyse if the following statement is true or false.

Then, we come across subsets. A subset S of another set A is defined as a set which contains element that belongs only to A. For example, {1} is a subset of {1,2}, then we write $\{ 1\} \subset \{ 1,2\}$.
We know that the null set {}, which is also denoted by $\phi$, is a subset of every set.
The given statement is $\phi \in \{ a,b\}$, that is {} belongs to {a, b}, meaning {} is an element of the set {a, b} which is wrong because $\phi$ is a subset of {a, b} and not an element itself.
$\phi \subset \{ a,b\}$
Note: You may wrongly conclude that $\phi \in \{ a,b\}$ is the correct statement which is wrong. You might also rewrite the statement as $\phi \notin \{ a,b\}$, which is also a correct answer.